My mom taught me to use baking soda, steel wool, and a LOT of elbow grease. I've saved a couple of pots that way.

You read my mind...or rather your mother did. I use one of those copper kitchen dish scrubbers with baking soda. Sometimes just a plastic scrubber with the baking soda works. I find it doesn't even take that much elbow grease, but maybe mine don't get as burned. My husband though is famous for burning his tea water in my best pans.

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I've never knitted anything I could recognize when it was finished. Actually, I've never finished anything, much to my family's relief.

I have also had luck, with baking sheets, with coating it in *bacon grease* and letting it sit, warm, for a day or two. Scrape with a plastic scraper, then wash as normal. Has gotten a layer of burnt off stuff off all the way to the metal.

ETA when I say warm, I mean, I leave it on my gas stove, over the pilot light, so it's warm to the touch but not hot. You might want to try putting in plastic and putting it in a sunny spot if you have an electric range.

I've rescued a few pots by simmering water and a dryer sheet for a couple hours. Even burned on rice came off effortlessly. And by burned on, I mean my son forgot about the rice long enough that the rice actually caught fire. (He did the same thing a few months later with grits. I was unable to rescue the pan).

My first attempt always begins by placing a dryer sheet in the pot, covering and letting it sit for ~24 hours. Then I move on to boiling diluted dish soap and oven cleaner.

Just the other day I had moderate success with this method:I put about 3/4 inch of water in the pot. I sprinkled in about 1/3 of a cup (it was a 3 quart pot) of baking soda. I swished it around and brought it to a boil. Then I turned off the heat and let it cool. Then I poured off the water (the baking soda was a thick paste) and used a scrubbing sponge, for about 3-5 minutes. All the black came off, but admittedly it doesn't look new... but then I had scorched it about 3 times previously and this was the first time I'd tried to actually do anything about it.